Abstract

The backscattering spectrum of spheres at flat interfaces viewed at small grazing angles depends upon reflections from the sphere's surface and the interface, as well as the sphere's elastic response and Franz wave contributions. For partially exposed spheres, one approach to modeling the reflective contribution is to extend the Kirchhoff approximation [K. Baik and P. L. Marston, IEEE J. Ocean. Eng. 33, 386–396 (2008)] to spheres. Laboratory measurements were carried out using short tone bursts for solid spheres at air-water and sand-water interfaces in such a way that it was typically possible to distinguish between the reflective and delayed elastic contributions viewed in the time domain. For spheres at an air-water interface, the reflective contributions have strong similarities with the Kirchhoff approximation while the strength of the delayed elastic contributions depends strongly on the extent of exposure of elastic guided wave coupling regions. The spectra of proud targets have similarities with image approximations, yielding ridges and valleys in the frequency versus grazing angle domain (associated with interference of contributions of similar magnitude), modulated by elastic contributions. Elastic contributions from small spheres near an air-water interface display a Lloyd's mirror pattern. [Work supported by ONR.]